{
  "abstract": "Kostochka and Thomason independently proved that every graph with density at least $β\\,t\\sqrt{\\log t}$ has a $K_t$ minor, for some constant $β$. Thomason later proved that the least such density is $(0.319\\ldots+o(1))\\,t\\sqrt{\\log t}$. However, the $o(1)$ term in this formula is not explicit, so the formula gives no bound for any specific value of $t$. The goal of this paper is a bound of the form $β\\,t\\sqrt{\\log t}$ that holds for every $t$, with $β$ small. We prove that, for every integer $t\\geqslant2$, every graph with density at least $4.5\\,t\\sqrt{\\log t}$ has a $K_t$ minor.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.41060",
  "author_total": 1,
  "authors": [
    {
      "name": "David R. Wood"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/26n3k9m2be1k8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.41060",
  "fulltext_url": null,
  "id": "26n3k9m2be1k8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.41060",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.41060",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/26n3k9m2be1k8.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2610.41060",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.41060"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "An explicit bound on the extremal function for complete graph minors",
  "title_text": "An explicit bound on the extremal function for complete graph minors",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:52Z",
  "url": "https://research.draconitic.com/paper/26n3k9m2be1k8",
  "venue": "arXiv",
  "versions": []
}